In computer numerically controlled (CNC) machining, a tool-head moves along a trajectory relative to a work-piece according to a pattern to machine a work-piece. The pattern can include straight, curved, open and closed contours. Of special interest to the invention are disconnected contours. The machining can include various types of processing of the work-piece, such as cutting or drilling the work-piece. For simplicity of explanation and without loss of the generality, the process of cutting the work-piece using a laser cutting machine.
Cutting features from sheet material according to the pattern is a common manufacturing process. Generally, a cutting head of a laser cutting machine is translated in a plane along, orthogonal axes. Laser cutters of this type are often used to cut discreet features from sheets of materials, e.g., plastic and metal sheets of varying thickness. Control of the laser cutter is usually performed by a computer numerical controller (CNC) following a prescribed set of instructions, e.g., implemented as “NC-code,” or “G-code.”
If the pattern to be cut includes disconnected contours) then the machining alternates with repositioning, e.g., after a cut the machine turns off the cutter, traverses a path to a new location, and turns the cutter on to continue the machining. Thus, as defined herein, a path is a special trajectory, usually straight, between two disconnected contours, while the cutter is off.
The trajectories of the machine are based on the pattern, e.g., a representation of all the contours to be cut. Some of the contours can be closed to represent a shape to be cut out of the material. The planning problem can determine a minimum-time or minimum-energy for all the cuts, among other formulations.
Until recently, all machining was characterized by stop-and-start motions. During the machining, the cutting head traverses along a path to an entry point of a contour of the pattern, stops, turns on the cutter, and then proceeds with the next contour. Consequently the fastest cut-to-cut traverse paths are straight lines. The planning problem for “stop-start” machining includes determining jointly an order of the cuts and the shortest straight traverse paths between the cuts.
However, the “stop-start” behavior of the laser cutter presumed by the trajectories limits the production rate of the machine. For high-speed machining, numerous accelerations and decelerations impose a high energy cost, and can wear out the machine.
Advances in cutting technologies uses “on-the-fly” cutting, that is, without stopping to turn the cutter on or off. This enables faster processing, but also poses a much more complicated planning problem, because straight traverses in on-the-fly machining can be suboptimal. However, substituting the straight traverses with other type of traverses can also be suboptimal, because that solution does not fully consider dynamical properties of the machine, see, e.g., U.S. Pat. No. 6,609,044. Other solutions involve hand-drawn trajectories, but obviously this is not a practical method for large planning problems.
A limiting factor on the production rate of an electromechanical machine, such as laser cutting machine, is directly related to the inertia of the mechanical components of the laser-cutting machine, e.g., the actuators. Therefore, reduction of the effective inertia of the components has a direct impact on the productivity of the laser-cutting machine. Such reduction can be achieved, in part, by using redundant actuators along each trajectory.
In the related U.S. application Ser. No. 13/535,266, a traveling salesman problem (TSP) is solved by determining a set of costs representing operations of a machine along a set of trajectories connecting a set of exit and entry points on contours of a pattern. Each trajectory represents an operation of the machine proceeding from an exit point with an exit velocity to an entry point with an entry velocity according to dynamics of the machine. The set of trajectories includes at least one trajectory representing the operation along a contour with non-zero velocities at corresponding exit and entry points, and at least one path representing the operation between different contours with non-zero velocities at the corresponding exit and entry points. A sequence of the trajectories optimizing a total cost of operation of the machine tracking the pattern is determined based on the costs, and a set of instructions for controlling the machine is determined according to the sequence.